LYAPUNOV-SCHMIDT REDUCTION IN THE ANALYSIS OF BIFURCATION SOLUTIONS AND CAUSTIC OF NONLINEAR SYSTEM OF ALGEBRAIC EQUATIONS
MURTADA JASSIM MOHAMMED *
Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah, Iraq
*Author to whom correspondence should be addressed.
In this paper bifurcation analysis and Bifurcation diagram of the nonlinear system (bifurcation equation) have been studied. Also, by using local method of Lyapunov-Schmidt we showed that the bifurcation equation corresponding to the elastic beams equation of sixth order is given by the nonlinear system of four quadratic equations.
Keywords: Nonlinear system, bifurcation diagram, Lyapunov-Schmidt method, regular solutions